Abstract
In this study, closure relations for total and turbulent convection fluxes of flame surface density and scalar dissipation rate were developed (i) by placing the focus of consideration on the flow velocity conditioned to the instantaneous flame within the mean flame brush and (ii) by considering the limiting behavior of this velocity at the leading and trailing edges of the flame brush. The model was tested against direct numerical simulation (DNS) data obtained from three statistically stationary, one-dimensional, planar, premixed turbulent flames associated with the flamelet regime of turbulent burning. While turbulent fluxes of flame surface density and scalar dissipation rate, obtained in the DNSs, showed the countergradient behavior, the model predicted the total fluxes reasonably well without using any tuning parameter. The model predictions were also compared with results computed using an alternative closure relation for the flame-conditioned velocity.
Highlights
Among various approaches to modeling premixed turbulent combustion, concepts that deal with a transport equation for the mean flame surface density (FSD) hΣi = h|∇c|i [1,2] or the Favre-averaged scalar dissipation rate (SDR) hχi~ = hρD∇c·∇ci/hρi [3] have become popular over the past decade [4,5,6]
As reviewed elsewhere [4,5,6], in applications, the turbulent transport terms are commonly modeled invoking a paradigm of gradient diffusion, for example, hu0 Σ0 i = −Dt ∇hΣi and hρu”χ”i =
In the statistically 1D, planar, and stationary case, huiu = huiu (x) and huib = huib (x) if the x-axis is normal to the mean wave, with averaging being performed over transverse planes
Summary
Among various approaches to modeling premixed turbulent combustion, concepts that deal with a transport equation for the mean flame surface density (FSD) hΣi = h|∇c|i [1,2] or the Favre-averaged scalar dissipation rate (SDR) hχi~ = hρD∇c·∇ci/hρi [3] have become popular over the past decade [4,5,6]. C is the combustion progress variable, which characterizes the state of a reacting mixture in a flame, and is equal to zero and unity in unburned reactants and equilibrium combustion products, respectively, ρ is the mixture density, D is the molecular diffusivity of c, and hqi and hqi~ = hρqi/hρi designate the Reynolds and Favre (i.e., mass-weighted), respectively, mean values of an arbitrary quantity q. At least for the turbulent flux hρu”c”i
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